AIMS Lie Groups: Fall-2022
Practice Exercises 10 : Due 10 Fri 16 Dec

1. Commutators in $\mathfrak{su}(3)$ S0 4491S
   1. Verify several of the commutators of the (real version of the) Gell-Mann matrices given in GELG. In each case, interpret your answer in terms of the root diagram. Repeat until you are comfortable with the relationship between your algebraic computation and the geometry of the root diagram.
   2. Use the root diagram to predict the direction of the commutator of \(L_+=\lambda_1-\mu_2\) with \(M_+=\lambda_4-\mu_5\), that is, guess the answer up to an overall numerical factor.
   3. Compute this commutator and compare it with your guess.